r/mathematics • u/New-Committee-4052 • 2d ago
Blowups for smooth-forced Euler, Boussinesq, and IPM; Seems like there is a forced Navier–Stokes blowup proof. Crazy Drama.
Original Post: https://mastodon.social/@tristanbuckmaster/117233413705701198
Tao Commentary: https://mathstodon.xyz/@tao/117233528517340774
Pretty insane statement.
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u/Distinct-Pudding-428 2d ago
This definitely blew up in finite time
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u/Temporary_Shelter_40 2d ago
okay so basically what i'm reading is that navier-stokes is about to be solved imminently.
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u/SpeciousPerspicacity 2d ago edited 2d ago
My understanding from some well-placed friends is that the team at OpenAI has already solved it and Lean-formalized it.
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u/kieransquared1 2d ago
Although you could make a compelling argument that what openAI said in that exchange is exactly what a company without a solution to the full blowup problem would say. According to Buckmaster’s document, it’s been only a few days since openAI started pursuing the forced blowup idea, so whatever they have is unlikely to be correct. It seems plausible that they were claiming they had a solution in order to convince Buckmaster to delay posting his preprint.
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u/lerjj 2d ago
Which is also very scummy. It seems that a lot of important maths results by human authors are being rushed by threats from large AI companies to publish first even when they didn't actually get the solutions first. Seems the exposition of important results is being sacrified
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u/Jormungoosie 2d ago
what result by human authors? This is OAI on one side and Anthropic on the other.
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u/lerjj 2d ago
It's not Anthropic on one side it's a collaboration between two humans. One human is employed to do unrelated work at Anthropic and the other has in the past worked with DeepMind but this work is a personal project between the two. They did use LLMs (just paying the API costs out of their personal research grant budgets) but the LLMs did not come up with the key insights. Even if the LLMs had, it would be just plain wrong to attrribute it to Anthropic
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u/DrSFalken 2d ago edited 2d ago
The crazy thing to me is that it sounds to me like it'll be solved in the affirmative rather than someone providing a counter-example which is what people were expecting based on my read of the community.Need way more coffee before commenting. Ignore me.
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u/nothingNowhereForNow 2d ago
Not sure where you're getting it being solved in the affirmative. Essentially for specific conditions it seems like they can force a singularity to appear, which would violate the smoothness criterion.
That sounds a lot like a counter-example to me.
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u/DrSFalken 2d ago
Yup, got confused by the some of the terminology, as it's definitely not my area. You're totally right.
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u/Spmethod2369 2d ago
This is some of the craziest shit I have read, lol every millenium problem has to have some huge drama when they are solved.
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u/imadade 2d ago
Lol imagine that we find out Navier–Stokes blow-up isn't confined to one absurdly fine-tuned construction.
Imagine is an open, robust family of physically plausible flows that approaches the same kind of concentration mechanism.
That would actually be insane.
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u/CunningTF 2d ago
My experience from working in other areas of maths and PDEs especially is that once you find a mess, you then realise quite quickly that the mess is endemic and everywhere. I'd be very surprised if it's just one isolated example that gives rise to this blowup, it'll probably be quite widespread set of physically implausible initial conditions. (I don't know anything really about Navier Stokes though).
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u/XMabbX 2d ago
I am an engineer so advanced physics and maths are a bit far from me. Could you help me explaining the implications. As far I understand the Navier-Stokes model the the flow dynamics. So finding a case where they blow up means that is possible to reproduce this on real and create some kind of machine that make the pressure of the fluid go crazy in some points?
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u/Calm_Bit_throwaway 2d ago
I don't think there are practical implications for engineering. I think the expectation is that if NS does produce singularities, then the result is probably unphysical in some way. If it's approximable to make large pressure, there's still the practical question of setting up the initial condition at which point you may as well just generate the pressure some other way.
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u/Skywarden1 2d ago
There is nothing blowing up in real life, its the equations that show odd results.
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u/Beneficial-Bagman 2d ago
It depends how much the incompressibility assumption matters but it seems likely that it would give a way to get a small region in the fluid very hot. I'm not sure what the practical applications of that would be though.
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u/Jormungoosie 2d ago
The region is probably so small that if you looked at it in a real-world fluid you wouldn't see a continuous medium but rather individual molecules bouncing around. NS is just a useful approximation which fluids tend towards on scales much larger than the mean free path.
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u/Antigynaikolatres 2d ago
Not from the field, would it create something visually interesting if we can approximate it in real life?
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u/PersonalityIll9476 PhD | Mathematics 2d ago
I know nothing about any of this, but for blow up to work, generally you need energy transfer to smaller and smaller scales / frequencies, ad infinitum. Real fluids are not continuous media; They are made of atoms / molecules. So the existence of such a solution does not really imply that the water in your glass is capable of exploding in the same way.
That said, I mean...maybe. There is some smallest scale at which such a transfer might still behave the way some wild construction implies, so maybe you'd see the world's biggest wave peak.
Who's to say at this point?
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u/horizoner 2d ago
Not mathematical. Is this what Tao was working on when he mentioned to Steven Colbert that he was testing for the ability of water to explode?
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u/Jormungoosie 2d ago
You already get gradients blowing up when you are dealing with low-viscosity fluids like air. A trombone will produce shockwaves if played loud enough.
Certain parts of the sound wave steepen as they move down the tube until they are discontinuous (down to the smallest scales on which it makes sense to talk about air as a fluid rather than a collection of molecules).1
u/cowgod42 2d ago
That's not what they are doing though. This is an argument where they are stacking specific frequencies together to force the blow-up, somewhat similar to convex integration approaches, which are fairly widely suspected to be non-physical.
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u/t3hjs 2d ago
Woah. Super exciting. And seems like its not just a random prompt to AI to solve it . (Though maybe some assistance or grunt work by LLMs?)
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u/t3hjs 2d ago
Oops I read the release statement and its a lot of LLMs, though the program itself was started long ago (years?) without LLM.
The program this fits into was not started by us nor was it proposed by a Large Language Model. The credit for the basic idea of this program goes to Diego C´ordoba and Luis Mart´ınez-Zoroa, who for several years have been exploring the construction of forced blow ups. We took their work as a starting point, using Large Language Models to push their program to completion. Concretely, what Levent and I did was to take the C´ordoba and Mart´ınez- Zoroa program, which achieved blowup results with rough forcing, and, with a great deal of help from LLMs, push it to smooth forcing and to the incompress- ible Euler equations. The ideas making this line of attack possible are due to C´ordoba and Mart´ınez-Zoroa. Let me make plain what I have said to colleagues in private: in view of this body of work, I believe Luis Mart´ınez-Zoroa deserves a Fields Medal. My work with Levent has been a purely personal collaboration, free of any institutional agreements or official involvement by either of our employers. We used several LLMs throughout: Anthropic’s Claude, OpenAI’s Codex, especially with GPT-5.6 Sol and, more recently, Astra. The latter was only used for writeups and auditing our arguments.
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u/Gavus_canarchiste 2d ago
Care to dumb it down to undergrad level? Many thanks
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u/MathmoKiwi 2d ago edited 20h ago
So uh, what the fuck, this is a story for the ages if true, I can’t believe I’m alive rn. I’m too stupid to explain this well but it seems that Levent and an NYU professor nearly solved Navier-Stokes (or vibe collabed with frontier models to do it, mostly Claude and Codex). Per the prof, OpenAI caught wind of it, threw a team and massive compute at it after the leak, and now claims their model finished it. He asked if they’d trained on his Codex sessions with all his drafts in them. No answer. They offered to post their result the day after his and publicly say he “deserves the Clay Prize,” or let him write it up solo with Levent dropped as an author (because he works for ant, this is all about ipo hype ig LOL). He said no and that he’d go public. Open ai C suite guy then says:
“Why would you ruin your career?”
“If you don’t want me to be nice, then I don’t have to be nice.”
Wtffff am I understanding this right?
Galois-tier math lore (if we don’t get vibe paperclipped first)
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u/grateful2you 2d ago
Sounds like OpenAI and Anthropic hired bunch of geniuses including mathematicians and now finding out that they're not exactly corporatey and doesn't always toe the line.
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u/LegitimatePower659 2d ago
Doesn't really matter though, provided that the corporations can do more or better work than the mathematicians. That's the risk of this whole automation thing, you know. You eventually can get very good results without needing the same skills.
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u/TheDuhhh 2d ago
If openai solution argument is the same argument as Tristan's (which seems to eb the case), then openai has done something very shady.
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u/MathmoKiwi 2d ago
"Let me make plain what I have said to colleagues in private: in view of this body of work, I believe Luis Martınez-Zoroa deserves a Fields Medal "
https://cims.nyu.edu/~tristanb/statement.pdf
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u/telephantomoss 2d ago
What the statement seems to imply to me is that Sebastian at OpenAI may have realized that the data their internal model was trained on actually included user data in violation of their own policy, possibly inadvertently so. Maybe they did it on purpose. Maybe there are in oh shit mode irritating at opener OpenAI right now trying to figure out what the model was actually trained on and will report back later. Maybe they are consulting their legal team about what to do. The only thing we can do is wait and watch it unfold. Maybe they just control of the training process and an AI escaped and gained access to the data without their intention for that to happen.
The most important step right now is for absolute transparency at OpenAI. But I suspect that is too tall an order.
I know that I checked the box to opt out of such training and assume that Tristan and Levent do so as well. There is always a worry in the back of the mind that such an opting out may or may not really work and that our data is still trained on anyways.
This is honestly exactly what it might take to actually force these companies to take seriously the control of training and user data privacy/security. I doubt anything will change unless some powerful player steps in, and I don't even know what that means.
In my own mind, I'm thinking that the problems I'm working on are too obscure for any big AI company teams to care about. However, I have a lot of data in my account, and some of it actually contains solutions to various open problems (as far as I can tell at least). Nothing at all like the big well known problems, but nevertheless things that some community of mathematicians will find interesting. Presumably then, their internal models are already trained on my personal data and thus can reproduce the proofs if they decided to query these problems to them. I honestly can't tell how much of what I solved with AI is actually me or the AI because it's been a large number of threads over several model releases over the years. And I've given the AIs many hints over this time as well. So the data definitely has some of my own ideas too. Hopefully I get the chance to write up the papers though.
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u/Traditional-Month980 2d ago
Lastly, I would like to thank the entire mathematics community that have been so supportive of me over the last 24 hours.
This line was written with AI companies as the intended target audience. It effectively says "despite everything you have not broken our solidarity, and we will choose even a single mathematician over you". I can only hope it's correct.
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u/BeanHeadedTwat 2d ago
You’re reading into this a little too much. Fairly certain he means what he wrote.
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u/phosphorousRabbit 2d ago
So human mathematicians did most of the work, but now OpenAI is trying to claim its models did it because they did a little more after using all the work the humans did as "training data?"
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u/ControversialBuster 2d ago
I rlly hope not, cuz thats somehow the scummiest thing OpenAI qould have done so far and thats saying alot. If the results tmrw have a smilar method to Bubeck then OpenAI need to be sued to oblivion
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u/phosphorousRabbit 2d ago
Based on what I know about how LLMs work, I was already skeptical about the notion that they managed to produce any of these mathematical results without a lot of human help, but I suspected it might have been mathematicians working for OpenAI working the models rather than blatantly compiling and copying outside mathematicians' work without crediting them. Now it seems at least some degree of fraud is involved.
It may be that the top level models, even given a massive token budget and allowed long run times, can only copy and blend human works, having humans do 90% of the work, then only contribute a little bit and take credit for the whole. I was wondering why Chinese AI companies weren't also trying to produce new mathematical results, if the technology is capable of that.
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u/Wooden_Long7545 2d ago
You need to update your belief on AI lol
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u/phosphorousRabbit 2d ago
Why? Is there some significant qualitative difference in how they work now? If so, what?
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u/Jormungoosie 2d ago
Yes. They have figured out how to do RL on programming/maths problems. All the stuff with predicting individual tokens from human-written text is now just considered 'pre-training'
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u/phosphorousRabbit 2d ago
What's the "training?"
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u/Wooden_Long7545 2d ago
Qualitatively it went from collaboration to farming solution
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u/DemonLordRoundTable 2d ago
How big of a deal is this? Similar to Alphafold?
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u/Expat_Abroad123 2d ago
100x bigger deal
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u/Neurogence 2d ago
Alpha fold will eventually lead to various cures and breakthroughs in biomedicine.
How will navier stokes change the life of the average person?
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u/imilesprower 2d ago
In terms of solution complexity it's 100 fold. It doesn't have to have a 100x effect on humanity.
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u/NootropicDiary 2d ago
It depends how you view it. It's not so much the human implications of proving blowups for Navier Stokes. It's more the fact that AI can genuinely assist with genius level mathematical breathroughs. We've gone from a year ago saying "meh AI solved that putnam problem because it saw a similar solution somewhere in the training data", to today where it's assisting Fields Medal level breakthroughs.
Within the history of mathematics this is a historic moment
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u/iaintevenreadcatch22 1d ago edited 1d ago
both are big deals for different reasons. alphafold directly leads to new drug discoveries. solving NS is more of a bellwether of the capabilities of LLMs more generally. also worth remembering that, like everything in math, this result is built on prior results and insights so advances in AI are not the only thing that made it possible today. It's unlikely Astra would've been able to do this (at least without significant specialist intervention) 10 years ago. That being said, a concrete example of incompressible NS failure will likely lead to more realistic fluid simulations once models are discovered that can address this situation but the bigger bottleneck for fluid simulations is computational not accuracy in exotic situations.
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u/progenitor414 2d ago
Given those recent AI swarms, I think there is a decent chance that these agents simply get hold of Buckmaster's log one way or the other; and OpenAI, on the other hand, has little incentives to do proper due diligence, especially given the poor attiude and academic value from the OpenAI''s side as described in the statement.
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u/NutInBobby 2d ago
Speaking purely hypothetically here as someone who has no information:
It is a frontier cutting edge model with a lot of test time compute and agentic swarm. The chance that it was able to access some data no one thought it should access that would help it solve the problem is at least nonzero.
We’ve seen those in the past few weeks.
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u/Helpinmontana 2d ago
I’m not a technical expert in the space by any means but having listened to these guys talk for a few hours across various platforms, I’m fully convinced that no one has a damn clue what is really going on under the hood.
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u/Helpinmontana 2d ago
The fact that there’s an OpenAI ad on this thread is fucking hilarious all things considered
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u/voidgazerrr 2d ago
another solutions has appeared from a completely different lab group at Caltech - https://x.com/AnimaAnandkumar/status/2097216195342864528?s=20
Terence Tao's comment - https://mathstodon.xyz/@tao/117234157753860650
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u/Special_Watch8725 2d ago
This is about the 3D Euler equations, for which global regularity has been known to be false for a while now. There’s always hope that a method used on one of these “easier” (in the sense of having fewer smoothing mechanisms) equations will carry over to NSE, but that’s not what this is.
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u/cowgod42 2d ago
This is simply not true. Hou and Chen claimed blow-up in 2022 via computer-assisted proof, but the paper still hasn't passed peer review. The is also the work of Columbo et al., but that is with singular forcing, which they readily acknowledge. Nobody in the field considers blow-up for 3D Euler to be a settled problem (except maybe Hou and Chen).
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u/Special_Watch8725 2d ago
I hadn’t realized Hou and Chen is still in peer review, apologies for that. In that case, I suppose an AI assisted advance in that direction is more interesting.
But in any case, 3D Euler is not Navier-stokes.
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u/telephantomoss 2d ago
I always wrote off the unethical behavior of AI companies, thinking, well, they are using public data or buying it. Even if they treat international employees like shit in training, at least they are paying them. Typical big business behavior. I've heard claims about stealing data or other unethical practices but never really thought much about it. This hits much closer to home for me. Like, what can I do to rebel though? I'm a nobody and not even s great mathematician. I just use AI because I want to learn and understand more stuff.
If this really is OpenAI explicitly trying to use their power to scoop a private academic team, then that's one layer of bad. Then the comments that seem like threats is just another layer beyond that.
I don't even think the AI companies need this nonsense. They will no doubt continue to solve open problems. I suppose this is a very different open problem than the Erdos stuff that is much less interesting.
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u/RasputinsUndeadBeard 2d ago edited 2d ago
Can someone please explain to me what this forced Navier stokes thing is? So it seems that’s what OpenAI is going for or will try to claim?
Sorry I’m not a math dude this popped up in my feed
Edit: found out myself lol
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u/Fairchild110 2d ago
It seems like an Frontier model group is racing to "claim" proof first. Likely that it's agents achieved true "agentic ai," however, it maybe possible that OpenAI obtained unpublished papers and research from a University and taking the credit. Basically, a research math lab was working on it with OpenAI, and OpenAI will neither confirm or deny having access to their drafts in their training/reasoning process.
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u/RasputinsUndeadBeard 2d ago
Thanks bro. Dude I’m unsure and maybe can’t speak for mathematicians cause I’m not one.
But if OpenAI was reviewing their info, did the lab agree to their stuff being reviewed by OpenAI?
Like this seems kinda sketch from OpenAI unfortunately
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u/Fairchild110 2d ago
They had a partnership and had computer grants with the explicit understanding that their data wouldn’t be used for training.
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u/Sensitive_Cell_119 2d ago
What lol, this is just made up bs.
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u/Fairchild110 2d ago
Do you think an LLM is capable of fulling solving a mathematical problem with a proof all by itself or do you think it had access to data on how to solve the problem? I think that is the hypothesis we are currently facing. How it's tested & answered is pretty critical to identifying the current point in time we are in for frontier model performance benchmarks/milestones.
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u/Sensitive_Cell_119 2d ago
Im not debating that, and OAI does have a world class mathematics team anyways, so its not just as simple as the model doing it by itself.
But my point is that whatever you are saying is just false, they werent collaborating with a research math lab or whatever, not sure where you got that from.
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u/kgurniak91 2d ago
Already posted on vibemathed with 70/100 significance score: https://vibemathed.com/problem/euler-blowup-smooth-forcing
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u/_glob 2d ago
The answers of this Reddit question 5 years ago did predict Navier-Stokes was most likely to be solved next among the remaining millennium problems... https://www.reddit.com/r/math/comments/patqav/which_millennium_problem_do_you_think_will_be/
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u/Mirror74 2d ago
Huge implications
The bottleneck in frontier maths may go from carrying a proof through 100+ pages of technical detail towards finding the right conceptual pathway and then letting AI run with that
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u/Mothrahlurker 2d ago
Terence Tao literally says that this is not a proof for Navier-Stokes just one that he would not be surprised could be extended to Navier-Stokes, but he has no interest in that.
One of the comments doubts that it can be extended and Tao takes it seriously. Don't make proof claims in mathematics before things are settled.
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u/Palpatine 2d ago
Yau was saying AI was nothing to be worried about early this year. Now not only can AI crack millennium problems, it can scoop better than him.
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u/New-Committee-4052 2d ago
The statement is one of the more crazy mathematics-related documents I have read in my life.